Minimal Reachability is Hard To Approximate

In this note, we consider the problem of choosing which nodes of a linear dynamical system should be actuated so that the state transfer from the system's initial condition to a given final state is possible. Assuming a standard complexity hypothesis, we show that this problem cannot be efficiently solved or approximated in polynomial, or even quasi-polynomial, time

Interpreting neural computations by examining intrinsic and embedding dimensionality of neural activity

The current exponential rise in recording capacity calls for new approaches for analysing and interpreting neural data. Effective dimensionality has emerged as a key concept for describing neural activity at the collective level, yet different studies rely on a variety of definitions of it. Here we focus on the complementary notions of intrinsic and embedding dimensionality, and argue that they provide a useful framework for extracting computational principles from data. Reviewing recent works, we propose that the intrinsic dimensionality reflects information about the latent variables encoded in collective activity, while embedding dimensionality reveals the manner in which this information is processed. Network models form an ideal substrate for testing more specifically the hypotheses on the computational principles reflected through intrinsic and embedding dimensionality

Low-dimensional controllability of brain networks

Network controllability is a powerful tool to study causal relationships in complex systems and identify the driver nodes for steering the network dynamics into desired states. However, due to ill-posed conditions, results become unreliable when the number of drivers becomes too small compared to the network size. This is a very common situation, particularly in real-world applications, where the possibility to access multiple nodes at the same time is limited by technological constraints, such as in the human brain. Although targeting smaller network parts might improve accuracy, challenges may remain for extremely unbalanced situations, when for example there is one single driver. To address this problem, we developed a mathematical framework that combines concepts from spectral graph theory and modern network science. Instead of controlling the original network dynamics, we aimed to control its low-dimensional embedding into the topological space derived from the network Laplacian. By performing extensive simulations on synthetic networks, we showed that a relatively low number of projected components is enough to improve the overall control accuracy, notably when dealing with very few drivers. Based on these findings, we introduced alternative low-dimensional controllability metrics and used them to identify the main driver areas of the human connectome obtained from N=6134 healthy individuals in the UK-biobank cohort. Results revealed previously unappreciated influential regions compared to standard approaches, enabled to draw control maps between distinct specialized large-scale brain systems, and yielded an anatomically-based understanding of hemispheric functional lateralization. Taken together, our results offered a theoretically-grounded solution to deal with network controllability in real-life applications and provided insights into the causal interactions of the human brain

Neurofeedback: principles, appraisal and outstanding issues

Neurofeedback is a form of brain training in which subjects are fed back information about some measure of their brain activity which they are instructed to modify in a way thought to be functionally advantageous. Over the last twenty years, NF has been used to treat various neurological and psychiatric conditions, and to improve cognitive function in various contexts. However, despite its growing popularity, each of the main steps in NF comes with its own set of often covert assumptions. Here we critically examine some conceptual and methodological issues associated with the way general objectives and neural targets of NF are defined, and review the neural mechanisms through which NF may act, and the way its efficacy is gauged. The NF process is characterised in terms of functional dynamics, and possible ways in which it may be controlled are discussed. Finally, it is proposed that improving NF will require better understanding of various fundamental aspects of brain dynamics and a more precise definition of functional brain activity and brain-behaviour relationships.Comment: 12 page

Drug-resistant focal epilepsy in children is associated with increased modal controllability of the whole brain and epileptogenic regions

Network control theory provides a framework by which neurophysiological dynamics of the brain can be modelled as a function of the structural connectome constructed from diffusion MRI. Average controllability describes the ability of a region to drive the brain to easy-to-reach neurophysiological states whilst modal controllability describes the ability of a region to drive the brain to difficult-to-reach states. In this study, we identify increases in mean average and modal controllability in children with drug-resistant epilepsy compared to healthy controls. Using simulations, we purport that these changes may be a result of increased thalamocortical connectivity. At the node level, we demonstrate decreased modal controllability in the thalamus and posterior cingulate regions. In those undergoing resective surgery, we also demonstrate increased modal controllability of the resected parcels, a finding specific to patients who were rendered seizure free following surgery. Changes in controllability are a manifestation of brain network dysfunction in epilepsy and may be a useful construct to understand the pathophysiology of this archetypical network disease. Understanding the mechanisms underlying these controllability changes may also facilitate the design of network-focussed interventions that seek to normalise network structure and function

Controllability in complex brain networks

Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures. Recently it has been proposed to characterize brain networks in terms of their "controllability", drawing on concepts and methods of control theory. The thesis will review the control theory for networks and its application in neuroscience. In particular, the study will highlight important limitations and some warning and caveats in the brain controllability framework.ope

Interictal Network Dynamics in Paediatric Epilepsy Surgery

Epilepsy is an archetypal brain network disorder. Despite two decades of research elucidating network mechanisms of disease and correlating these with outcomes, the clinical management of children with epilepsy does not readily integrate network concepts. For example, network measures are not used in presurgical evaluation to guide decision making or surgical management plans. The aim of this thesis was to investigate novel network frameworks from the perspective of a clinician, with the explicit aim of finding measures that may be clinically useful and translatable to directly benefit patient care. We examined networks at three different scales, namely macro (whole brain diffusion MRI), meso (subnetworks from SEEG recordings) and micro (single unit networks) scales, consistently finding network abnormalities in children being evaluated for or undergoing epilepsy surgery. This work also provides a path to clinical translation, using frameworks such as IDEAL to robustly assess the impact of these new technologies on management and outcomes. The thesis sets up a platform from which promising computational technology, that utilises brain network analyses, can be readily translated to benefit patient care

Reduced emergent character of neural dynamics in patients with a disrupted connectome

High-level brain functions are widely believed to emerge from the orchestrated activity of multiple neural systems. However, lacking a formal definition and practical quantification of emergence for experimental data, neuroscientists have been unable to empirically test this long-standing conjecture. Here we investigate this fundamental question by leveraging a recently proposed framework known as “Integrated Information Decomposition,” which establishes a principled information-theoretic approach to operationalise and quantify emergence in dynamical systems — including the human brain. By analysing functional MRI data, our results show that the emergent and hierarchical character of neural dynamics is significantly diminished in chronically unresponsive patients suffering from severe brain injury. At a functional level, we demonstrate that emergence capacity is positively correlated with the extent of hierarchical organisation in brain activity. Furthermore, by combining computational approaches from network control theory and whole-brain biophysical modelling, we show that the reduced capacity for emergent and hierarchical dynamics in severely brain-injured patients can be mechanistically explained by disruptions in the patients’ structural connectome. Overall, our results suggest that chronic unresponsiveness resulting from severe brain injury may be related to structural impairment of the fundamental neural infrastructures required for brain dynamics to support emergence